ACT Past Papers with Answers

Paper 17

ACT April 2021

Form Z04 · Math Test · 60 questions

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

5 times as much as he gets paid during regular time. Thomas works 46 hours in 1 week and gets $117 in deductions taken out of his pay for this week. After the deductions are taken out, how much of Thomas’s pay for this week remains?

A$492B$573C$609D$618E$735

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

Which of the following expressions is equivalent to −4x3 − 12x3 + 9x2 ? + 9x2 + 9x2 + 9x2

A0 0x8B0−7x8C0−8x3D−16x3E−16x6

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

When x = 2, 10 + 3_12 ÷ (3x)+ =0?

A012B016C026D034E104

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

⎪6 − 4⎪ − ⎪3 − 8⎪ = ? 1 _ _ 9 1 __ _ 15 6 __ _ 15 7 __ _ 15 8 __ _ 15 DO YOUR FIGURING HERE. 14 GO ON TO THE NEXT PAGE.

A−7B−3C3D7E21

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

The expression (4c − 3d)(3c + d) is equivalent to: − 13cd − 3d2 − 13cd + 3d2 − 05cd − 3d2 − 05cd + 3d2 − 03d2

A12c2B12c2C12c2D12c2E12c2

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

Of the 180 students in a college course, of the students earned an A for the course, of the students earned a B for the course, and the rest of the students earned a C for the course. How many of the students earned a C for the course?

A075B090C105D120E135

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

The number of fish, f, in Skipper’s Pond at the beginning of each year can be modeled by the equation f(x) = 3(2x ), where x represents the number of years after the beginning of the year 2000. For example, x = 0 represents the beginning of the year 2000, x = 1 represents the beginning of the year 2001, and so forth. According to the model, how many fish were in Skipper’s Pond at the beginning of the year 2006 ?

A000,96B00,192C00,384D01,458E46,656

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

Manish drove from Chicago to Baton Rouge. At 8:00 a.m., he was 510 km from Baton Rouge. At 1:00 p.m., he was 105 km from Baton Rouge. Which of the following values is closest to Manish’s average speed, in kilometers per hour, from 8:00 a.m. to 1:00 p.m. ? 1 _ _ 4 1 _ _ 3 DO YOUR FIGURING HERE. 15 GO ON TO THE NEXT PAGE. ACT-Z04 2 2

A058B068C081D094E102

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

In the figure shown below, E and G lie on AC ___ , D and F lie on AB ___ , DE ___ and FG ___ are parallel to BC ___ , and the given lengths are in feet. What is the length of AC ___ , in feet?

A13B26C29D42E48

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

Katerina runs 15 miles in 2 hours. What is the average number of minutes it takes her to run 1 mile?

A06B10C12D16E17

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

A bag contains 8 red marbles, 9 yellow marbles, and 7 green marbles. How many additional red marbles must be added to the 24 marbles already in the bag so that the probability of randomly drawing a red marble is ? D F 7 6 8 16 B C G E A 1 _ _ 2 1 _ _ 2 2 _ _ 3 1 _ _ 2 3 _ _ 5 DO YOUR FIGURING HERE. 16 GO ON TO THE NEXT PAGE. ACT-Z04 2 2

A11B16C20D24E32

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

In the standard (x,y) coordinate plane, the point (2,1) is the midpoint of CD ___ . Point C has coordinates (6,8). What are the coordinates of point D ?

A1−2,− 2B(−2,−6)C1 4, 2D(10, 10)E(10, 15)

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

At his job, the first 40 hours of each week that Thomas works is regular time, and any additional time that he works is overtime. Thomas gets paid $15 per hour during regular time. During overtime Thomas gets paid

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AChoice A — see source imageBChoice B — see source imageCChoice C — see source imageDChoice D — see source imageEChoice E — see source image

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

At Sweet Stuff Fresh Produce the price of a bag of grapes depends on the total number of bags purchased at 1 time, as shown in the table below. In 2 trips to Sweet Stuff this week, Janelle purchased 3 bags of grapes on Monday and 4 bags of grapes on Wednesday. How much money would Janelle have saved if she had instead purchased 7 bags of grapes in 1 trip on Monday?

A$0.20B$1.00C$1.40D$2.00E$2.50

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

What is 3% of 4.14 × 104 ? Number of bags Price per bag 1−3 $3.00 4−6 $2.80 7−9 $2.60 10 or more $2.50 7 _ _ 2 9 _ _ 2 DO YOUR FIGURING HERE. 17 GO ON TO THE NEXT PAGE. ACT-Z04 2 2 DO YOUR FIGURING HERE. 18 GO ON TO THE NEXT PAGE. ACT-Z04 2 2 16. What value of x satisfies the equation −3(4x − 5) = 2(1 − 5x) ?

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A001,242B001,380C012,420D013,800E124,2006−7−8−19Choice J — see source image10Choice K — see source image

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

Source question 16. Refer to the source image.

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AChoice F — see source imageBChoice G — see source imageCChoice H — see source imageDChoice J — see source imageEChoice K — see source image

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

In right triangle nABC shown below, the given lengths are in millimeters. What is sin,A ?

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AChoice A — see source imageBChoice B — see source imageCChoice C — see source imageDChoice D — see source imageEChoice E — see source image

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

1 2 − = ?

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A−B−CChoice H — see source imageDChoice J — see source imageEChoice K — see source image

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

Loto begins at his back door and walks 8 yards east, 6 yards north, 12 yards east, and 5 yards north to the barn door. About how many yards less would he walk if he could walk directly from the back door to the barn door? 13 __ _ 2 4√" 2 ____ _ 9 4√" 2 ____ _ 7 7√" 2 ____ _ 8 7 _ _ 9 9 _ _ 7 27 __ _ 64 2 _ _ 3 9 __ _ 16 9 __ _ 32 9 __ _ 32 16 __ _ 9 32 __ _ 9 9 7 4√" 2 A C B 3 __ _ 17 17 __ _ 22 17 __ _ 2

A08B19C23D26E31

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

For a given set of data, the standard score, z, corresponding to the raw score, x, is given by z = , where μ is the mean of the set and σ is the standard deviation. If, for a set of scores, μ = 78 and σ = 6, which of the following is the raw score, x, corresponding to z = 2 ?

A90B84C80D76E66

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

In the figure below, A, B, C, and D lie on the circle centered at O. Which of the following does NOT appear in the figure?

AAcute triangleBEquilateral triangleCIsosceles triangleDRight triangleEScalene triangle

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

What is the slope of a line, in the standard (x,y) coordinate plane, that is parallel to x + 5y = 9 ?

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A−5B−CChoice H — see source imageDChoice J — see source imageE9

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

Given y = and x > 1, which of the following is a possible value of y ? A 60° O B C D 1 _ _ 5 1 _ _ 5 9 _ _ 5 x _____ x − 1 x − μ ____ _ σ DO YOUR FIGURING HERE. 19 GO ON TO THE NEXT PAGE. ACT-Z04 2 2 DO YOUR FIGURING HERE. 20 GO ON TO THE NEXT PAGE. ACT-Z04 2 2 24. The set of all positive integers that are divisible by both 15 and 35 is infinite. What is the least positive integer in this set?

A−1.9B−0.9C0.0D0.9E1.9600570508105921010525

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

Source question 24. Refer to the source image.

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AChoice F — see source imageBChoice G — see source imageCChoice H — see source imageDChoice J — see source imageEChoice K — see source image

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

In nABC shown below, the measure of ∠A is 58°, and AB ___ ≅ AC ___ . What is the measure of ∠C ?

A32°B42°C58°D61°E62°

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

About 1.48 × 108 square kilometers of Earth’s surface is land; the rest, about 3.63 × 108 square kilometers, is water. If a returning space capsule lands at a random point on Earth’s surface, which of the following is the best estimate of the probability that the space capsule will land in water?

A80%B71%C65%D41%E29%

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

On the first 7 statistics tests of the semester, Jamal scored 61, 76, 79, 80, 80, 84, and 91. The mean, median, and mode of his scores were 79, 80, and 80, respectively. On the 8th statistics test, Jamal scored 90. How do the mean, median, and mode of all 8 of his scores compare to the mean, median, and mode of his first 7 scores? Mean Median Mode 58° ? B A C

Aequal greater greaterBgreater greater greaterCgreater greater equalDgreater equal greaterEgreater equal equal

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

The solid rectangular prism shown below was built by alternating congruent black cubes and white cubes such that 2 cubes of the same color have at most 1 edge touching. What is the total number of white cubes that were used to build the prism?

A045B102C105D140E210

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

One side of square ABCD has a length of 12 meters. A certain rectangle whose area is equal to the area of ABCD has a width of 8 meters. What is the length, in meters, of the rectangle?

A12B16C18D20E24

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

The average of a list of 4 numbers is 92.0. A new list of 4 numbers has the same first 3 numbers as the original list, but the fourth number in the original list is 40, and the fourth number in the new list is 48. What is the average of this new list of numbers?

A81.0B92.0C94.0D94.4E96.6

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

The vector i represents 1 mile per hour east, and the vector j represents 1 mile per hour north. Maria is jogging south at 12 miles per hour. One of the following vectors represents Maria’s velocity, in miles per hour. Which one? DO YOUR FIGURING HERE. 21 GO ON TO THE NEXT PAGE. ACT-Z04 2 2 DO YOUR FIGURING HERE. 22 GO ON TO THE NEXT PAGE. ACT-Z04 2 2 32. Four identical glasses are shown below. One glass is empty, and the other 3 glasses are full, full, and full of water, respectively. If the water were redistributed equally among the 4 glasses, what fractional part of each glass would be filled?

Source page for act-april-2021-form-z04-math-031

A−12iB−12jC012iD012jE012i + 12j6Choice F — see source image7Choice G — see source image8Choice H — see source image9Choice J — see source image10Choice K — see source image

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

Source question 32. Refer to the source image.

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AChoice F — see source imageBChoice G — see source imageCChoice H — see source imageDChoice J — see source imageEChoice K — see source image

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

Aurelio is purchasing carpet tiles to cover an area of his living room floor that is 8 feet wide by 10 feet long. Each carpet tile is a square 20 inches wide by 20 inches long. What is the minimum number of carpet tiles that Aurelio must purchase to cover this area of his living room floor?

A05B11C21D30E84

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

In the standard (x,y) coordinate plane, a circle with its center at (8,5) and a radius of 9 coordinate units has which of the following equations? + (y − 5)2 = 81 + (y − 5)2 = 09 + (y + 5)2 = 81 + (y + 5)2 = 09 + (y + 8)2 = 81 2 __ _ 11 8 __ _ 11 3 __ _ 22 31 __ _ 60 31 __ _ 80 1 _ _ 3 4 _ _ 5 1 _ _ 2 1 _ _ 4 Many humans carry the gene Yq77. The Yq test determines, with 100% accuracy, whether a human carries Yq77. If a Yq test result is positive, the human carries the Yq77 gene. If a Yq test result is negative, the human does NOT carry Yq77. Sam designed a less expensive test for Yq77 called the Sam77 test. It produces some incorrect results. To determine the accuracy of the Sam77 test, both tests were administered to 1,000 volunteers. The results from this administration are summarized in the table below.

A(x − 8)2B(x − 8)2C(x + 8)2D(x + 8)2E(x + 5)2

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

It cost $2,500 to administer each Yq test and $50 to administer each Sam77 test. What was the total cost to administer both tests to all the volunteers?

A$1,537,500B$1,556,750C$1,568,250D$2,500,000E$2,550,000

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

What percent of the volunteers actually carry Yq77 ?

A57.5%B60.0%C60.5%D61.5%E62.5%

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

For how many volunteers did the Sam77 test give an incorrect result?

A010B025C035D385E400

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

One of the volunteers whose Sam77 test result was positive will be chosen at random. To the nearest

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

Source question 39. Refer to the source image.

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AChoice A — see source imageBChoice B — see source imageCChoice C — see source imageDChoice D — see source imageEChoice E — see source image

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

Regardless of how the graph is oriented in the standard (x,y) coordinate plane, NO graph in one of the following categories has a vertical line of symmetry. Which one?

ALineBSquareCPentagonDParallelogramEScalene triangle

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

The equation 24x2 + 2x = 15 has 2 solutions. What is the greater of the 2 solutions?

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AChoice A — see source imageBChoice B — see source imageCChoice C — see source imageDChoice D — see source imageEChoice E — see source image

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

Which of the following expressions is equal to (sin,60°)(cos,30°) + (cos,60°)(sin,30°) ?

Acos(60° − 30°)Bcos(60° + 30°)Csin(60° − 30°)Dsin(60° + 30°)Esin1 2

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

What is the area, in square units, of a circle that has a circumference 12π units long? −2 −1 3 _ _ 4 4 _ _ 3 5 _ _ 6 7 _ _ 6 11 __ _ 15 60° + 30° ________ 2 DO YOUR FIGURING HERE. 25 GO ON TO THE NEXT PAGE. ACT-Z04 2 2 44. A barrel contains 25 liters of a solvent mixture that is 40% solvent and 60% water. Lee will add pure solvent to the barrel, without removing any of the mixture currently in the barrel, so that the new mixture will contain 50% solvent and 50% water. How many liters of pure solvent should Lee add to create this new mixture?

A006πB012πC024πD036πE144π602.5705810912.51015

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

Source question 44. Refer to the source image.

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

For all x ≠ ±y, + = ? + y2

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AChoice A — see source imageBChoice B — see source imageCChoice C — see source imageDx2EChoice E — see source image

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

Mary, James, and Carlos sold -page advertisements for the school yearbook. Mary sold twice as many as Carlos did, and James sold 3 times as many as Mary did. What fraction of these advertisements did Carlos sell?

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AChoice F — see source imageBChoice G — see source imageCChoice H — see source imageDChoice J — see source imageEChoice K — see source image

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

In a window display at a flower shop, there are 3 spots for 1 plant each. To fill these 3 spots, Emily has 6 plants to select from, each of a different type. Selecting from the 6 plants, Emily can make how many possible display arrangements with 1 plant in each spot? (Note: The positions of the unselected plants do not matter.) x + y _____ 2x x2 + y2 ______ x2 − y2 1 _ _ 4 1 _ _ 9 1 _ _ 7 1 _ _ 6 1 _ _ 5 1 _ _ 3 y ____ _ x − y x ____ _ x + y 1 _____ x − y x + y _____ x − y DO YOUR FIGURING HERE. 26 GO ON TO THE NEXT PAGE. ACT-Z04 2 2 The quadratic function f and nMPQ are graphed in the standard (x,y) coordinate plane below. Points M(2a, 5b), N(4a, 9b), and P(6a, 5b) are on f. Point Q(4a, 0) is NOT on f.

A003B006C015D120E216

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

In terms of a and b, what is the area, in square coordinate units, of nMPQ ?

A08abB10abC12abD15abE20ab

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

Point M will remain fixed, and point Q will move to the right along the x-axis. As Q continues to move to the right, which of the following statements describes what will happen to the slope of MQ __ __ ?

AIt will decrease and eventually be negative.BIt will decrease but never be negative.CIt will stay the same.DIt will increase but never be positive.EIt will increase and eventually be positive.

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

One of the following values is equal to f(5a). Which one? y x 2a 4a 6a 8a O 8b 6b 4b 2b N M P Q f Use the following information to answer questions 48–50. DO YOUR FIGURING HERE. 27 GO ON TO THE NEXT PAGE. ACT-Z04 2 2 51. Twelve jurors are needed for an upcoming trial. The diagram below illustrates a part of the process of jury selection. The 12 jurors will be selected from a jury pool of about 60 people. The court records show a trend that only 40% of the people who are summoned for jury duty actually appear and that of the people who appear, are excused. If this same trend continues, how many people should be summoned to have as close as possible to 60 people in the jury pool?

A3aB5aC5bD8aE8b604570908150922510800

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

Source question 51. Refer to the source image.

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AChoice A — see source imageBChoice B — see source imageCChoice C — see source imageDChoice D — see source imageEChoice E — see source image

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

What is the 275th digit after the decimal point in the repeating decimal 0.6295 ____ _ ?

A0B2C5D6E9

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

Given that f(x) = x2 − 4 and g(x) = x + 3, what are all the values of x for which f_g(x)+ = 0 ?

A−5 and −1B−3, −2, and 2C−1 and 1D01 and 5E−√" 5 and √" 5

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

Given that p is a positive number, n is a negative number, and ⎪p⎪ > ⎪n⎪, which of the following expressions has the greatest value? ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ Summoned Did not appear Appeared Excused Jury pool p − n _____ p p − n _____ n p + n _____ p − n p + n _____ p 1 _ _ 3 p + n _____ n

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AChoice F — see source imageBChoice G — see source imageCChoice H — see source imageDChoice J — see source imageEChoice K — see source image

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

If i = √"" −1, then = ?

A−3B−1C0D01E03

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

In one of the following graphs in the standard (x,y) coordinate plane, the solution set to the system of inequalities below is shown shaded. Which one? x + 2y ≤ 6 53x2 > 12 − 3y2

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AChoice F — see source imageBChoice G — see source imageCChoice H — see source imageDChoice J — see source imageEChoice K — see source image

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

Let a, b, c, and d be real numbers. Given that ac = 1, is undefined, and abc = d, which of the following must be true? x y O x y O x y O x y O x O y F. b + c _____ d 1 _ _ 2 i + i2 + i3 _________ i3 + i4 + i5 DO YOUR FIGURING HERE. 28 GO ON TO THE NEXT PAGE. ACT-Z04 2 2

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Aa = 0 or c = 0Ba = 1 and c = 1Ca = −cDb = 0Eb + c = 06Choice K — see source image7Choice J — see source image8Choice H — see source image9Choice G — see source image

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

A cosine function is shown in the standard (x,y) coordinate plane below. One of the following equations represents this function. Which one?

Ay = 2 cos1 2By = 2 cos(3x)Cy = 3 cos1 2Dy = 3 cos1 2Ey = 3 cos(2x)

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

The figure below shows a flying kite. At a certain moment, the kite string forms an angle of elevation of 75° from point A on the ground. At the same moment, the angle of elevation of the kite at point B, 240 ft from A on level ground, is 45°. What is the length, in feet, of the string?

A060√" 3B080√" 6C144D180E240

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Paper 17 · ACT April 2021 · Form Z04 · Math Test

If a publisher charges $15 for the first copy of a book that is ordered and $12 for each additional copy, which of the following expressions represents the cost of y books? π _ _ 2 y x O 1 x _ _ 3 x _ _ 3 x _ _ 2 45° 75° string kite 240 A B DO YOUR FIGURING HERE. 29 ACT-Z04 2 2 END OF TEST 2 STOP! DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURN TO THE PREVIOUS TEST.

A12y + 03B12y + 15C15y − 03D15y + 03E15y + 12

Form Z04 · Math Test · 60 questions

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